Educational devices in the form of balances for teaching algebraic principles are known. One such balance, described in U.S. Pat. No. 784,145 to Donecker, includes four receptacles, or pans, adapted for receiving weights, with two receptacles disposed on either side of the balance. The balance is intended for use with weights of known mass which represent integer values and weights of "unknown," but marked, mass which represent variables. In use, an imbalance between the two sides of the device causes a lever, or balance beam, to tilt from its horizontal equilibrium position, thereby indicating an algebraic inequality in the demonstrated expression. The '145 device advantageously permits various algebraic principles to be visually and interactively demonstrated, including the subtraction and multiplication of positive and negative quantities and the solving of equations.
A similar four-pan balance is described in U.S. Pat. No. 3,000,114 to Orlov. However, the '114 balance further includes a visual indicator with which the equality or inequality of the demonstrated expression is indicated. Thus, instead of determining the relative equality of the demonstrated expression by a visual assessment of whether or not the lever is horizontal as in the '145 balance, the '114 visual indicator provides an easy-to-read indication of such condition.
One limitation of conventional balances however, is their dependence on the precision of the mass of the weights. This is because any deviation from the expected mass of the weights can result in a false indication of inequality, even when the two sides of the modeled expression are algebraically balanced. While the tolerance of the weight mass can be tightened with the use of precise manufacturing techniques and/or strict quality control, these requirements generally increase the cost of the weights. Further, even with the most precise manufacturing techniques and strict quality control, some tolerance in the mass of the weights is generally unavoidable.